Compound of five cuboctahedra
In geometry, this uniform polyhedron compound is a composition of 5 cuboctahedra. It has icosahedral symmetry Ih.
| Compound of five cuboctahedra | |
|---|---|
 | |
| Type | Uniform compound |
| Index | UC59 |
| Polyhedra | 5 cuboctahedra |
| Faces | 40 triangles, 30 squares |
| Edges | 120 |
| Vertices | 60 |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | pyritohedral (Th) |
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±2, 0, ±2)
- (±τ, ±τ−1, ±(2τ−1))
- (±1, ±τ−2, ±τ2)
where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
References
- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.
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